Contract design and stability in many-to-many matching

We develop a model of many-to-many matching with contracts which subsumes as special cases many-to-many matching markets and buyer–seller markets with heterogeneous and indivisible goods. In our setting, substitutable preferences are sufficient to guarantee the existence of stable outcomes; moreover, in contrast to results for the setting of many-to-one matching with contracts, if any agent’s preferences are not substitutable, then the existence of a stable outcome cannot be guaranteed. We show that bundling contractual primitives encourages substitutability of agents’ preferences over contracts; however, such bundling also makes the contractual language less expressive. Thus, we see that, in choosing contract language, market designers face a tradeoff between expressiveness and stability. JEL Codes: C78, C62, D47, L14